How to have a part move from one place to another?

So I was watching a few videos on how to make a script to make an object go up and down and one going from left to right but to no avail they would end up glitching or not doing anything or just completely misbehaving. Would someone mind helping me please.

Here is the set up I have then I will show you the script I used last. So one object above is called Part1 and an object below is called Part2 and the object that needs to be moving when the game starts is called MovingPart. Also they are grouped together and the group is called Moving. So once the game starts Moving part is supposed to fuse into the part that I set it to in the script in this case I chose Part1. Then from there it goes to Part2. Then in the code was added while true do so I can make it last forever. The problem is this one does nothing when the game starts. Please help here is the script:

local bodyposition = script.Parent.MovingPart.BodyPosition
local p1 = script.Parent.Point1
local p2 = script.Parent.Point2

bodyposition.Position = p1.Position

while true do
    wait(3)
    bodyposition.Position = p1.Position
    wait(3)
    bodyposition.Position = p2.Position
end